BM= boatswains mate. Very difficult work on the deck of the ship, you are doing all the hardwork when the boat comes in and leaves port. You have to know tons of knots and be really on top of things. The BMs I know have been stalled at e-5 for a really long time b/c it's a closed rate and a few have been forced to re-rate b/c of the same reason. Not a lot of quals for civ world. But those dudes have some of the most pride of any rate, they really boast about that job b/c it's really hardwork and most wouldn't be able to take the long haul. Almost every single BM I know has a pair of crossed anchors tattooed somewhere on his body.
DC= Damage Controlman lot of ship work. You have to be DC qualified and then make sure your shipmates are as well. On the ship you will do tons of drills to prepare you in case of an attack or a system failure. You deal with shipboard fires, leaks, plumbing, like a handy man.
MR= Machinery Repairman? Don't know any but sounds pretty self explanatory
PR= "Parachute Rigger" really is Aircrew Survival Equipmentman. Your jobs can really range from anywhere to fixing parachutes to making sure survival radios are up to date. You work closely with AMEs who work with ejection seats. You make sure the survival equipment is in working order for the pilots, a lot of things weigh on your shoulders. I know PRs they have a lot of pride and they are some of the hardest working bad asses I know. They are tough, they don't take any sh!t.
ADD: To that person above me... the term is "stitch *****" and most Navy jobs in some way teach you job specific skills. For instance, I know a guy who worked in my rate (AT-I), got out and is now working for Samsung Technologies making 120k per year. But you have to realize you don't do your job very hands on until at least your 2nd tour if not 2nd enlistment and most employers know that, so plan on doing 8 years if you wanna get out with a job related to what you did in the Navy.
I dunno how FTS in these rates would differ from AD but I doubt it's by much, a job is a job.